In this paper we consider a fundamental problem in the area of viral marketing , called TARGET SET SELECTION problem. We study the problem when the underlying graph is a block-cactus graph, a chordal graph or a Hamming graph. We show that if G is a block-cactus graph, then the TARGET SET SELECTION problem can be solved in linear time, which generalizes… (More)
Distance-hereditary graphs are graphs in which every two vertices have the same distance in every connected induced subgraph containing them. This paper studies distance-hereditary graphs from an algorithmic viewpoint. In particular, we present linear-time algorithms for finding a minimum weighted connected dominating set and a minimum vertex-weighted… (More)
Let G be a graph with a threshold function θ : V (G) → N such that 1 ≤ θ(v) ≤ d G (v) for every vertex v of G, where d G (v) is the degree of v in G. Suppose we are given a target set S ⊆ V (G). The paper considers the following repetitive process on G. At time step 0 the vertices of S are colored black and the other vertices are colored white. After that,… (More)
The domination problem and its variants have been extensively studied in the literature. In this paper we investigate the domination problem in distance-hereditary graphs. In particular, we give a linear-time algorithm for the domination problem in distance-hereditary graphs by a labeling approach. We actually solve a more general problem, called the… (More)
A graph is distance-hereditary if the distance between any two vertices in a connected induced subgraph is the same as in the original graph. This paper presents eecient algorithms for solving the weighted connected k-domination and the weighted k-dominating clique problems in distance-hereditary graphs.
A graph is distance-hereditary if the distance between any two vertices in a connected induced subgraph is the same as in the original graph. In this paper, we study metric properties of distance-hereditary graphs. In particular, we determine the structures of centers and medians of distance-hereditary and related graphs. The relations between eccentricity,… (More)
In this paper we consider a fundamental problem in the area of viral marketing , called TARGET SET SELECTION problem. In a a viral marketing setting, social networks are modeled by graphs with potential customers of a new product as vertices and friend relationships as edges, where each vertex v is assigned a threshold value θ(v). The thresholds represent… (More)
It is shown that the difference between the chromatic number χ and the fractional chromatic number χ f can be arbitrarily large in the class of uniquely colorable, vertex transitive graphs. For the lexicographic product G • H it is shown that χ(G • H) ≥ χ f (G) χ(H). This bound has several consequences, in particular it unifies and extends several known… (More)